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# Geodesic Dome Notes & Calculator

written by Rene K. Mueller, Copyright (c) 2005, 2006, 2007, last updated Tue, January 29, 2019

### 5V 7/15 Icosahedron Dome

 Geodesic 5V 7/15 Icosahedron Dome (front view)
 Geodesic 5V 7/15 Icosahedron Dome (bird view)
• vertices/connectors: 126
• 25 x 4-way
• 6 x 5-way
• 95 x 6-way
•  5V 7/15 Icosahedron Dome Construction Map
• edges/struts & bending angles (αstrut):
• A x 30: 0.19815 (5.69°)
• B x 60: 0.22569 (6.48°)
• C x 30: 0.23160 (6.65°)
• D x 30: 0.23179 (6.66°)
• E x 50: 0.24509 (7.04°)
• F x 10: 0.24535 (7.05°)
• G x 60: 0.24724 (7.10°)
• H x 50: 0.25517 (7.33°)
• I x 30: 0.26160 (7.52°)
• total 350 struts (9 kinds)1)
• strut variance 32.1%
• faces: 225 (3-sided)
• A-A-D x 30 (54.19°, 54.19°, 71.61°)
• B-B-D x 30 (59.10°, 59.10°, 61.80°)
• B-C-G x 60 (56.13°, 58.44°, 65.43°)
• E-E-F x 20 (59.96°, 59.96°, 60.08°)
• E-G-H x 50 (58.37°, 59.18°, 62.45°)
• H-H-I x 25 (59.17°, 59.17°, 61.67°)
• I-I-I x 10 (60.00°, 60.00°, 60.00°)
• 7 kinds of faces2)
• height: 0.896 or 44.78% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

#### 5V 7/15 Icosahedron Dome Calculator

 Geodesic 5V 7/15 Icosahedron Dome (Human is 170cm/5'7")

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 30,
• Blath = x 60,
• Clath = x 30,
• Dlath = x 30,
• Elath = x 50,
• Flath = x 10,
• Glath = x 60,
• Hlath = x 50,
• Ilath = x 30,
• h =

Cut optimization:
• normalize Elath+Elath = 1.0, therefore Elath+Elath =
• cuts:
• 30 x (Alath+Glath):
• 50 x (Blath+Flath):
• 5 x (Blath+Blath):
• 60 x (Clath+Dlath):
• 30 x (Elath+Elath):
• total 175 laths to cut

### 5V 8/15 Icosahedron Dome

 Geodesic 5V 8/15 Icosahedron Dome (front view)
 Geodesic 5V 8/15 Icosahedron Dome (bird view)
• vertices/connectors: 151
• 25 x 4-way
• 6 x 5-way
• 120 x 6-way
•  5V 8/15 Icosahedron Dome Construction Map
• edges/struts & bending angles (αstrut):
• A x 30: 0.19815 (5.69°)
• B x 60: 0.22569 (6.48°)
• C x 30: 0.23160 (6.65°)
• D x 30: 0.23179 (6.66°)
• E x 80: 0.24509 (7.04°)
• F x 20: 0.24535 (7.05°)
• G x 70: 0.24724 (7.10°)
• H x 70: 0.25517 (7.33°)
• I x 35: 0.26160 (7.52°)
• total 425 struts (9 kinds)1)
• strut variance 32.1%
• faces: 275 (3-sided)
• A-A-D x 30 (54.19°, 54.19°, 71.61°)
• B-B-D x 30 (59.10°, 59.10°, 61.80°)
• B-C-G x 60 (56.13°, 58.44°, 65.43°)
• E-E-F x 40 (59.96°, 59.96°, 60.08°)
• E-G-H x 70 (58.37°, 59.18°, 62.45°)
• H-H-I x 35 (59.17°, 59.17°, 61.67°)
• I-I-I x 10 (60.00°, 60.00°, 60.00°)
• 7 kinds of faces2)
• height: 1.111 or 55.56% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

#### 5V 8/15 Icosahedron Dome Calculator

 Geodesic 5V 8/15 Icosahedron Dome (Human is 170cm/5'7")

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 30,
• Blath = x 60,
• Clath = x 30,
• Dlath = x 30,
• Elath = x 80,
• Flath = x 20,
• Glath = x 70,
• Hlath = x 70,
• Ilath = x 35,
• h =

### 6V Icosahedron Dome

 Geodesic 6V Icosahedron Dome (front view)
 Geodesic 6V Icosahedron Dome (bird view)
• vertices/connectors: 196
• 30 x 4-way
• 6 x 5-way
• 160 x 6-way
•  6V Icosahedron Dome Construction Map
• edges/struts & bending angles (αstrut):
• A x 30: 0.16257 (4.66°)
• B x 60: 0.18191 (5.22°)
• C x 30: 0.18738 (5.38°)
• D x 30: 0.19048 (5.47°)
• E x 60: 0.19801 (5.68°)
• F x 90: 0.20282 (5.82°)
• G x 130: 0.20591 (5.91°)
• H x 65: 0.21535 (6.18°)
• I x 60: 0.21663 (6.22°)
• total 555 struts (9 kinds)1)
• strut variance 33.2%
• faces: 360 (3-sided)
• A-A-D x 30 (54.14°, 54.14°, 71.72°)
• B-B-D x 30 (58.42°, 58.42°, 63.15°)
• B-C-F x 60 (55.40°, 58.00°, 66.60°)
• E-F-G x 120 (57.95°, 60.24°, 61.81°)
• G-G-H x 60 (58.46°, 58.46°, 63.08°)
• H-I-I x 60 (59.63°, 60.18°, 60.18°)
• 6 kinds of faces2)
• height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

#### 6V Icosahedron Dome Calculator

 Geodesic 6V Icosahedron Dome (Human is 170cm/5'7")

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 30,
• Blath = x 60,
• Clath = x 30,
• Dlath = x 30,
• Elath = x 60,
• Flath = x 90,
• Glath = x 130,
• Hlath = x 65,
• Ilath = x 60,
• h =

### 2V.3V Icosahedron Dome

 Geodesic 2V.3V Icosahedron Dome (front view)
 Geodesic 2V.3V Icosahedron Dome (bird view)
• vertices/connectors: 196
• 30 x 4-way
• 6 x 5-way
• 160 x 6-way
•  2V.3V Icosahedron Dome Construction Map
• edges/struts & bending angles (αstrut):
• A x 60: 0.18212 (5.22°)
• B x 30: 0.18854 (5.41°)
• C x 60: 0.18922 (5.43°)
• D x 60: 0.18932 (5.43°)
• E x 60: 0.19125 (5.49°)
• F x 70: 0.20591 (5.91°)
• G x 30: 0.21321 (6.12°)
• H x 60: 0.21445 (6.16°)
• I x 65: 0.21535 (6.18°)
• J x 60: 0.21663 (6.22°)
• total 555 struts (10 kinds)1)
• strut variance 18.9%
• faces: 360 (3-sided)
• A-A-G x 30 (54.17°, 54.17°, 71.66°)
• A-C-F x 60 (54.69°, 57.98°, 67.33°)
• B-D-H x 60 (55.23°, 55.58°, 69.19°)
• C-E-H x 60 (55.22°, 56.15°, 68.63°)
• D-D-G x 30 (55.73°, 55.73°, 68.54°)
• E-E-I x 30 (55.74°, 55.74°, 68.53°)
• F-F-I x 30 (58.46°, 58.46°, 63.08°)
• I-J-J x 60 (59.63°, 60.18°, 60.18°)
• 8 kinds of faces2)
• height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

#### 2V.3V Icosahedron Dome Calculator

 Geodesic 2V.3V Icosahedron Dome (Human is 170cm/5'7")

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 60,
• Blath = x 30,
• Clath = x 60,
• Dlath = x 60,
• Elath = x 60,
• Flath = x 70,
• Glath = x 30,
• Hlath = x 60,
• Ilath = x 65,
• Jlath = x 60,
• h =

The 2V.3V has 10 kinds of strut lengths, and 18.7% strut variance - compared to 6V with 9 kinds and 33.3% variance. So, you might think about prefering more even triangles, choose 2V.3V or less struth kinds then the 6V.

### 3V.2V Icosahedron Dome

The 3V.2V Icosahedron could also be used to achieve the same amount of subdivision, yet, the 3V is a bit uneven around the base, and the 2nd stage of 2V doesn't even this again, so the base isn't even, yet, 7 kinds of struts. I won't list the details as I won't recommend 3V.2V over 2V.3V or 6V at all.

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Creative Commons (CC) BY, SA, NC 2005-2017, developed, designed and written by René K. Müller,
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